Shame on many of the respondents to this post - and some compliments.
1. To the original poster, you need to carefully reason your statements. Force of law is irrelevant at the point of being asked to leave the property. Second, do you really want Delaware to adopt the Texas debacle of 30.06 legally enforced signage barring carry?? Google 30.06 and have fun.
2. One poster suggested asking the manager the law as one banker dubiously referenced FDIC businesses. Seriously? If you knew what you were doing you would address such a 'communication' to the GENERAL COUNSEL of the party in mention. However, that likely will not end well.
Unlike retailers who have largely deferred to "state carry laws" many financial institutions are explicitly hostile to the 2A to the point of denying service to those in the firearms sector. Then lets take this a step further, Delaware is politically owned by banks. By failing to exercise tact this is not going to end well for us as these bank lobbies (still) own the Delaware Congress. We already lost open carry at meetings of the people (city & municipal halls), banks would be the next easy target to muzzle us.
TACT and DIPLOMACY people! My response would have been nothing referring to the illegality of the signage. I agree in the request to complete my transaction, vacate the premises henceforth, and then think very carefully on writing a letter, or taking my business elsewhere.